Hopf分岔系统的参数化镇定方法  

Parametric Stabilization Method for a Class of Hopf Bifurcation Systems

作　　者：陆金波[1] 侯晓荣[1] 罗敏[1] 

机构地区：[1]电子科技大学能源科学与工程学院,成都611731

出　　处：《电子科技大学学报》2016年第6期944-949,共6页Journal of University of Electronic Science and Technology of China

基　　金：国家自然科学基金(61374001,61074189)

摘　　要：针对Hopf分岔系统镇定问题,提出了一种参数化镇定方法。应用该方法设计的控制器阶次较低,结构简单,不含有平衡点的值,不改变原系统平衡点的位置。添加控制器后能够较好地改善原系统分岔点附近的特性,实现对原系统的Hopf分岔甚至混沌状态的稳定控制。根据Hurwitz判据推导了参数化控制器的约束条件,并用柱形代数剖分算法求得了控制器的参数区间,在区间内任意一组参数都能够镇定系统的状态。以Lorenz系统为例,展开说明了该参数化镇定方法对控制器的设计过程,并进行了仿真。仿真结果验证了该方法的有效性。A parametric stabilization method is proposed for the problem of Hopf bifurcation system control. Compared with the existing methods, the controller designed by this method has a lower controller order and a simpler structure, and it does not contain equilibrium points. The method keeps equilibrium of the origin system unchanged. Under the control, the characteristics of the original system will be improved at equilibrium, and the system states of Hopf bifurcation or chaos can be controlled to stable. Using the Hurwitz criterion, the constraints of the parametric controller are derived. The idea of cylindrical algebraic decomposition （CAD） is employed to compute the constraints to find the parameter ranges of the designed controller, and the controller can be designed to stabilize the system by using any feasible control parameters in the ranges. Taking Lorenz system as an example, the controller design process of the method and numerical simulations are discussed. The simulation results show the effectiveness of the proposed method.

关 键 词：柱形代数剖分 Hopf分岔控制 LORENZ系统 参数化控制器 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]